Solve 9(5a-4b)^2-64c^2

$$9 ( 5 a - 4 b ) ^ { 2 } - 64 c ^ { 2 }$$

Expand

$$225a^{2}-360ab+144b^{2}-64c^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(5a-4b\right)^{2}.

$$9\left(25a^{2}-40ab+16b^{2}\right)-64c^{2}$$

Use the distributive property to multiply 9 by 25a^{2}-40ab+16b^{2}.

$$225a^{2}-360ab+144b^{2}-64c^{2}$$

Evaluate

$$9\left(5a-4b\right)^{2}-64c^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(5a-4b\right)^{2}.

$$9\left(25a^{2}-40ab+16b^{2}\right)-64c^{2}$$

Use the distributive property to multiply 9 by 25a^{2}-40ab+16b^{2}.

$$225a^{2}-360ab+144b^{2}-64c^{2}$$